Related papers: Default Logic and Bounded Treewidth
Many hard algorithmic problems dealing with graphs, circuits, formulas and constraints admit polynomial-time upper bounds if the underlying graph has small treewidth. The same problems often encourage reducing the maximal degree of vertices…
The linear induced matching width (LMIM-width) of a graph is a width parameter defined by using the notion of branch-decompositions of a set function on ternary trees. In this paper we study output-polynomial enumeration algorithms on…
We consider combinatorial problems that can be solved in polynomial time for graphs of bounded treewidth but where the order of the polynomial that bounds the running time is expected to depend on the treewidth bound. First we review some…
We investigate the computation of minimum-cost spanning trees satisfying prescribed vertex degree constraints: Given a graph $G$ and a constraint function $D$, we ask for a (minimum-cost) spanning tree $T$ such that for each vertex $v$, $T$…
We introduce the tree-decomposition-based parameter totally $\Delta$-modular treewidth (TDM-treewidth) for matrices with two nonzero entries per row. We show how to solve integer programs whose matrices have bounded TDM-treewidth in…
We design a proof system for propositional classical logic that integrates two languages for Boolean functions: standard conjunction-disjunction-negation and binary decision trees. We give two reasons to do so. The first is…
Algorithmic meta-theorems state that problems definable in a fixed logic can be solved efficiently on structures with certain properties. An example is Courcelle's Theorem, which states that all problems expressible in monadic second-order…
Prioritized default reasoning has illustrated its rich expressiveness and flexibility in knowledge representation and reasoning. However, many important aspects of prioritized default reasoning have yet to be thoroughly explored. In this…
Treewidth is a measure of how tree-like a graph is. It has many important algorithmic applications because many NP-hard problems on general graphs become tractable when restricted to graphs of bounded treewidth. Algorithms for problems on…
We study optimal decision policies for integer linear programs with a fixed feasible set and varying cost vectors, represented as linear decision trees. Once synthesized for a given feasible set, they return an optimal solution for any…
Linear model trees are regression trees that incorporate linear models in the leaf nodes. This preserves the intuitive interpretation of decision trees and at the same time enables them to better capture linear relationships, which is hard…
The notion of treewidth, introduced by Robertson and Seymour in their seminal Graph Minors series, turned out to have tremendous impact on graph algorithmics. Many hard computational problems on graphs turn out to be efficiently solvable in…
We consider network design problems with deadline or delay. All previous results for these models are based on randomized embedding of the graph into a tree (HST) and then solving the problem on this tree. We show that this is not…
In the Weighted Treewidth-$\eta$ Deletion problem we are given a node-weighted graph $G$ and we look for a vertex subset $X$ of minimum weight such that the treewidth of $G-X$ is at most $\eta$. We show that Weighted Treewidth-$\eta$…
The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…
The local tree-width of a graph G=(V,E) is the function ltw^G: N -> N that associates with every natural number r the maximal tree-width of an r-neighborhood in G. Our main graph theoretic result is a decomposition theorem for graphs with…
Two major difficulties in using default logics are their intractability and the problem of selecting among multiple extensions. We propose an approach to these problems based on integrating nommonotonic reasoning with plausible reasoning…
Decision trees are widely used for non-linear modeling, as they capture interactions between predictors while producing inherently interpretable models. Despite their popularity, performing inference on the non-linear fit remains largely…
We introduce the concept of a class of graphs, or more generally, relational structures, being locally tree-decomposable. There are numerous examples of locally tree-decomposable classes, among them the class of planar graphs and all…
Linear tree constraints were introduced by Hofmann and Rodriguez in the context of amortized resource analysis for object oriented programs. More precisely, they gave a reduction from inference of resource types to constraint solving. Thus,…